Yes, I would tend to agree with your observation, and I would advocate that no one should be allowed to take their animal into public areas without some means of certification that the animal is trained properly for the environment and conditions it is likely to encounter.

My whole point, though, is it is unfair to grant rights to one group of people and not to the rest of us. Service animals do typically receive a level of training that often includes some form of certification, and if the authorities were to allow the same for non-service animals, then at least we can hope for some measure of equality. To categorically exempt any one group from the restrictions and limitations imposed on the rest of us is and will always be just as discriminatory, debtrimental and costly to our society as when the reverse is allowed.